Find the Determinant [[1,2,4,8],[9,7,7,7],[3,7,7,6],[2,9,7,2]]

$[\begin{array}{c} 1 & 2 & 4 & 8 \\ 9 & 7 & 7 & 7 \\ 3 & 7 & 7 & 6 \\ 2 & 9 & 7 & 2 \end{array}]$

Step 1

Set up the determinant by breaking it into smaller components.

$1 | \begin{array}{c} 7 & 7 & 7 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Step 2

Find the determinant of $1 | \begin{array}{c} 7 & 7 & 7 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$7 | \begin{array}{c} 7 & 6 \\ 7 & 2 \end{array} | - 7 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $7 | \begin{array}{c} 7 & 6 \\ 7 & 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$7 ((7) (2) - 7 \cdot 6) - 7 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $7$ by $2$ .

$7 (14 - 7 \cdot 6) - 7 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $6$ .

$7 (14 - 42) - 7 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $42$ from $14$ .

$7 \cdot - 28 - 7 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $7$ by $- 28$ .

$- 196 - 7 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $- 7 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 196 - 7 ((7) (2) - 7 \cdot 7) + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $7$ by $2$ .

$- 196 - 7 (14 - 7 \cdot 7) + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $7$ .

$- 196 - 7 (14 - 49) + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $49$ from $14$ .

$- 196 - 7 \cdot - 35 + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $- 35$ .

$- 196 + 245 + 9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $9 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 196 + 245 + 9 ((7) (6) - 7 \cdot 7) - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $7$ by $6$ .

$- 196 + 245 + 9 (42 - 7 \cdot 7) - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $7$ .

$- 196 + 245 + 9 (42 - 49) - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $49$ from $42$ .

$- 196 + 245 + 9 \cdot - 7 - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $9$ by $- 7$ .

$- 196 + 245 - 63 - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Add $- 196$ and $245$ .

$49 - 63 - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Subtract $63$ from $49$ .

$- 14 - 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} | + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Step 3

Find the determinant of $- 9 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 6 \\ 9 & 7 & 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$- 14 - 9 (2 | \begin{array}{c} 7 & 6 \\ 7 & 2 \end{array} | - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $2 | \begin{array}{c} 7 & 6 \\ 7 & 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 - 9 (2 ((7) (2) - 7 \cdot 6) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $7$ by $2$ .

$- 14 - 9 (2 (14 - 7 \cdot 6) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $6$ .

$- 14 - 9 (2 (14 - 42) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $42$ from $14$ .

$- 14 - 9 (2 \cdot - 28 - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $2$ by $- 28$ .

$- 14 - 9 (- 56 - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $- 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 - 9 (- 56 - 7 ((4) (2) - 7 \cdot 8) + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $2$ .

$- 14 - 9 (- 56 - 7 (8 - 7 \cdot 8) + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $8$ .

$- 14 - 9 (- 56 - 7 (8 - 56) + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $56$ from $8$ .

$- 14 - 9 (- 56 - 7 \cdot - 48 + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $- 48$ .

$- 14 - 9 (- 56 + 336 + 9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $9 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 - 9 (- 56 + 336 + 9 ((4) (6) - 7 \cdot 8)) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $6$ .

$- 14 - 9 (- 56 + 336 + 9 (24 - 7 \cdot 8)) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $8$ .

$- 14 - 9 (- 56 + 336 + 9 (24 - 56)) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $56$ from $24$ .

$- 14 - 9 (- 56 + 336 + 9 \cdot - 32) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $9$ by $- 32$ .

$- 14 - 9 (- 56 + 336 - 288) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Add $- 56$ and $336$ .

$- 14 - 9 (280 - 288) + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Subtract $288$ from $280$ .

$- 14 - 9 \cdot - 8 + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 9$ by $- 8$ .

$- 14 + 72 + 3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} | - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Step 4

Find the determinant of $3 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 9 & 7 & 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$- 14 + 72 + 3 (2 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} | - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $2 | \begin{array}{c} 7 & 7 \\ 7 & 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 + 72 + 3 (2 ((7) (2) - 7 \cdot 7) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $7$ by $2$ .

$- 14 + 72 + 3 (2 (14 - 7 \cdot 7) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $7$ .

$- 14 + 72 + 3 (2 (14 - 49) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $49$ from $14$ .

$- 14 + 72 + 3 (2 \cdot - 35 - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $2$ by $- 35$ .

$- 14 + 72 + 3 (- 70 - 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} | + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $- 7 | \begin{array}{c} 4 & 8 \\ 7 & 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 + 72 + 3 (- 70 - 7 ((4) (2) - 7 \cdot 8) + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $2$ .

$- 14 + 72 + 3 (- 70 - 7 (8 - 7 \cdot 8) + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $8$ .

$- 14 + 72 + 3 (- 70 - 7 (8 - 56) + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $56$ from $8$ .

$- 14 + 72 + 3 (- 70 - 7 \cdot - 48 + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $- 48$ .

$- 14 + 72 + 3 (- 70 + 336 + 9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Find the determinant of $9 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 + 72 + 3 (- 70 + 336 + 9 ((4) (7) - 7 \cdot 8)) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $7$ .

$- 14 + 72 + 3 (- 70 + 336 + 9 (28 - 7 \cdot 8)) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $- 7$ by $8$ .

$- 14 + 72 + 3 (- 70 + 336 + 9 (28 - 56)) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Simplify the expression.

Subtract $56$ from $28$ .

$- 14 + 72 + 3 (- 70 + 336 + 9 \cdot - 28) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $9$ by $- 28$ .

$- 14 + 72 + 3 (- 70 + 336 - 252) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Add $- 70$ and $336$ .

$- 14 + 72 + 3 (266 - 252) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Subtract $252$ from $266$ .

$- 14 + 72 + 3 (14) - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Multiply $3$ by $14$ .

$- 14 + 72 + 42 - 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$

Step 5

Find the determinant of $- 2 | \begin{array}{c} 2 & 4 & 8 \\ 7 & 7 & 7 \\ 7 & 7 & 6 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$- 14 + 72 + 42 - 2 (2 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} | - 7 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} | + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Find the determinant of $2 | \begin{array}{c} 7 & 7 \\ 7 & 6 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 + 72 + 42 - 2 (2 ((7) (6) - 7 \cdot 7) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} | + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $7$ by $6$ .

$- 14 + 72 + 42 - 2 (2 (42 - 7 \cdot 7) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} | + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Multiply $- 7$ by $7$ .

$- 14 + 72 + 42 - 2 (2 (42 - 49) - 7 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} | + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Simplify the expression.

Subtract $49$ from $42$ .

$- 14 + 72 + 42 - 2 (2 \cdot - 7 - 7 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} | + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Multiply $2$ by $- 7$ .

$- 14 + 72 + 42 - 2 (- 14 - 7 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} | + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Find the determinant of $- 7 | \begin{array}{c} 4 & 8 \\ 7 & 6 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 + 72 + 42 - 2 (- 14 - 7 ((4) (6) - 7 \cdot 8) + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $6$ .

$- 14 + 72 + 42 - 2 (- 14 - 7 (24 - 7 \cdot 8) + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Multiply $- 7$ by $8$ .

$- 14 + 72 + 42 - 2 (- 14 - 7 (24 - 56) + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Simplify the expression.

Subtract $56$ from $24$ .

$- 14 + 72 + 42 - 2 (- 14 - 7 \cdot - 32 + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Multiply $- 7$ by $- 32$ .

$- 14 + 72 + 42 - 2 (- 14 + 224 + 7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |)$

Find the determinant of $7 | \begin{array}{c} 4 & 8 \\ 7 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 14 + 72 + 42 - 2 (- 14 + 224 + 7 ((4) (7) - 7 \cdot 8))$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $7$ .

$- 14 + 72 + 42 - 2 (- 14 + 224 + 7 (28 - 7 \cdot 8))$

Multiply $- 7$ by $8$ .

$- 14 + 72 + 42 - 2 (- 14 + 224 + 7 (28 - 56))$

Simplify the expression.

Subtract $56$ from $28$ .

$- 14 + 72 + 42 - 2 (- 14 + 224 + 7 \cdot - 28)$

Multiply $7$ by $- 28$ .

$- 14 + 72 + 42 - 2 (- 14 + 224 - 196)$

Add $- 14$ and $224$ .

$- 14 + 72 + 42 - 2 (210 - 196)$

Subtract $196$ from $210$ .

$- 14 + 72 + 42 - 2 \cdot 14$

Multiply $- 2$ by $14$ .

$- 14 + 72 + 42 - 28$

Step 6

Add $- 14$ and $72$ .

$58 + 42 - 28$

Step 7

Add $58$ and $42$ .

$100 - 28$

Step 8

Subtract $28$ from $100$ .

$72$

Find the Determinant [[1,2,4,8],[9,7,7,7],[3,7,7,6],[2,9,7,2]]

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